Glycolaldehyde Monomer and Oligomer Equilibria in Aqueous

Article pubs.acs.org/JPCA

Glycolaldehyde Monomer and Oligomer Equilibria in Aqueous Solution: Comparing Computational Chemistry and NMR Data Jeremy Kua,*,†,‡ Melissa M. Galloway,† Katherine D. Millage,† Joseph E. Avila,† and David O. De Haan† †

Department of Chemistry and Biochemistry, University of San Diego, 5998 Alcala Park, San Diego, California 92110, United States S Supporting Information *

ABSTRACT: A computational protocol utilizing density functional theory calculations, including Poisson−Boltzmann implicit solvent and free energy corrections, is applied to study the thermodynamic and kinetic energy landscape of glycolaldehyde in solution. Comparison is made to NMR measurements of dissolved glycolaldehyde, where the initial dimeric ring structure interconverts among several species before reaching equilibrium where the hydrated monomer is dominant. There is good agreement between computation and experiment for the concentrations of all species in solution at equilibrium, that is, the calculated relative free energies represent the system well. There is also relatively good agreement between the calculated activation barriers and the estimated rate constants for the hydration reaction. The computational approach also predicted that two of the trimers would have a small but appreciable equilibrium concentration (>0.005 M), and this was confirmed by NMR measurements. Our results suggest that while our computational protocol is reasonable and may be applied to quickly map the energy landscape of more complex reactions, knowledge of the caveats and potential errors in this approach need to be taken into account.

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INTRODUCTION Atmospheric aerosol impacts both climate change and human health.1−4 Secondary organic aerosol makes up a significant fraction of total particulate matter. Gas-phase oxidation chemistry drives its formation, as low volatility oxidation products partition from the gas to the condensed phase.5−7 In addition, highly water-soluble gases will partition into aqueous phase particles and droplets.8,9 Subsequent chemical processing in the condensed phase can alter the chemical and physical properties of the aerosol, further reducing the volatility of the chemical components. Many studies have attempted to elucidate these chemical processes, but it has been estimated that only ∼10% of the organic compounds within aerosol have been identified with current analytical methods.10 As climate change predictions must include the effects of aerosol particles reflecting sunlight and influencing cloud formation, it is necessary to improve scientific understanding of both the chemical and physical processes that occur within the atmospheric condensed phase in order to more accurately predict climate change.4,10 Many atmospheric condensed-phase compounds, such as carbonyls, are highly oxidized.10 The primary source of carbonyls in the atmosphere is the gas-phase oxidation of hydrocarbons,11,12 the most abundant of these being methane and isoprene.13 Glyoxal and methylglyoxal, the simplest alphadicarbonyls, are two of the most abundant aldehydes found in cloudwater and aqueous aerosol.14,15 Once in the cloud or aerosol, these aldehydes readily hydrate and can undergo oligomerization reactions to form a complex suite of molecules as water is lost through evaporation.16 The hydration process leads to higher effective Henry’s Law constants than would be © 2013 American Chemical Society

expected based on vapor pressure and physical solubility for these and similar aldehydes and increases the total aldehyde concentrations within clouds and aerosol.17 The impact of two other small water-soluble aldehydes, formaldehyde and glycolaldehyde, on aerosol has not been as well studied, but both have been identified as potentially important contributors to particulate matter. Formaldehyde is one of the most abundant atmospheric aldehydes, found in both the gas- and condensed-phase.15 Recent studies have shown that formaldehyde could impact brown carbon formation via its role in imidazole formation,18 but many of the reactions it undergoes within the aerosol are not well characterized. Gas-phase glycolaldehyde is produced through the gas-phase oxidation of anthropogenic19 and biogenic20−22 hydrocarbons and has been detected in biomass burning plumes.23,24 It is found in the gas phase at midpart-per-trillion to low-part-per-billion concentrations11,12,25−27 and in atmospheric water samples (e.g., clouds, fog, and aqueous aerosol).15,27 In the gas phase, hydroxyl radical (OH) oxidation and photolysis are the dominant loss processes, giving rise to an atmospheric lifetime of several hours to a day.26,28 Photolysis of condensed-phase glycolaldehyde is much less important than in the gas-phase due to the fact that ∼90% of glycolaldehyde is found in the hydrated, gem-diol form instead of the more reactive aldehyde form.28,29 Aqueous-phase oxidation of glycolaldehyde by OH forms glyoxal and oxidized acids (e.g., oxalic, glyoxylic, and glycolic).30,31 However, the aerosol Received: December 11, 2012 Revised: March 10, 2013 Published: March 11, 2013 2997

dx.doi.org/10.1021/jp312202j | J. Phys. Chem. A 2013, 117, 2997−3008

The Journal of Physical Chemistry A

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Figure 1. Glycolaldehyde monomers and dimers in solution.

implications of nonoxidative condensed-phase glycolaldehyde chemistry are still relatively unknown. The modeling study of Lim et al. found that glycolaldehyde uptake onto cloud droplets could contribute significantly to secondary organic aerosol formation through cloud processing.32 In laboratory studies of the aerosol uptake of isoprene oxidation products, Nguyen et al. observed possible oligomeric glycolaldehyde in the aerosol.33 Ortiz-Montalvo et al. found high aerosol yields from glycolaldehyde−OH mixtures in laboratory drying experiments.34 A single molecular species that can potentially selfoligomerize in solution may result in a very complex mixture depending on the reaction conditions. The oligomerization of concentrated solutions of formaldehyde is well known. Under neutral or acidic conditions, acetal/hemiacetal oligomers and oxane rings are observed35 and methanol is often added to aqueous formaldehyde solutions to prevent this oligomerization and oxidation.36 Under alkaline conditions, the formose reaction is operational, and a wide variety of C4−C7 sugars are observed; in addition, aldol condensation reactions compete with the Cannizzaro reaction under these conditions, further widening the product distribution.35 The formose reaction has also been implicated in origin-of-life chemistry as a potential route to ribose.37 Glycolaldehyde, which could be considered the dimer of formaldehyde formed by an aldol reaction, is the key player in the formose reaction because the reaction becomes autocatalytic once it is formed. Glycolaldehyde is readily available commercially in a dimeric hemiacetal form that leads to monomer formation and hydration upon dissolution in water.29

Unlike formaldehyde, which forms oligomers in a large size distribution,38 an aqueous 1 M solution of glycolaldehyde contains predominantly monomers and dimers. While there are just two monomeric species (the aldehyde and its hydrate), there are seven potential dimer structures in the mixture, that is, the system has some complexity, but remains tractable (see Figure 1). This provides a suitable test system for a computational protocol we have devised to map the thermodynamic and kinetic energy landscape of oligomerization reactions. Because of the large number of reactions that can take place leading to different products, and the difficulty in isolating intermediates, it can be a challenge to evaluate the viability of different reaction mechanisms. Computational chemistry is a powerful tool in this regard because we can calculate both the energetic stability of a wide range of potential intermediates and the activation energy barriers for different mechanistic pathways. We have previously applied this protocol to study the oligomerization of both glyoxal39 and methylglyoxal40 in solution. The protocol was justified based on reasonable agreement with experimental observations of the species observed by NMR, but there were few quantitative numbers to compare the relative accuracy of our computational results. At present, we are using the same protocol to map the rather complex energy landscape for formaldehyde oligomerization, but we wanted to verify the relative accuracy of our protocol by making a detailed comparison to a related, atmospherically relevant chemical system that remained tractable to study via NMR, hence our choice of glycolaldehyde. 2998



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Figure 2. Potential acyclic trimers and their formation reactions.

Figure 3. Potential glycolaldehyde cyclic trimers.

is this last assumption that is potentially problematic, which is why many computational studies utilizing electronic structure methods usually (1) restrict their comparisons to gas-phase systems if the free energies are being compared to experimental work, (2) report solution phase energies or enthalpies but not free energies, or (3) add an additional empirical correction to

In brief, our computational protocol uses relatively quick density functional theory gas-phase calculations to find the electronic energies, zero-point energies, and enthalpic corrections. The solution phase energies are obtained with a fast implicit Poisson−Boltzmann representation of the solvent, and the entropic correction in solution is simply half the gas-phase entropic correction as suggested by Abraham41 and Wertz.42 It 2999



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Table 1. Energies of Monomers, Dimers, Trimers and Transition State Structures Eelec (a.u.)

Esolv (kcal)

Hcorr (kcal)

Gcorr (kcal)

−0.5TScorr (kcal)

G298 (kcal)

2 3 ax/eq 4 trans 5 cis 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

−76.44744 −458.23664 −458.23735 −458.23348 −458.23754 −458.24133 −458.23643 −229.11010 −305.57126 −534.70852 −534.70226 −687.36805 −763.84149 −763.83346 −763.83002 −763.83119 −687.36505 −687.36268 −687.36771 −687.36521 −687.36341 −687.36620 −687.36307 −687.36841

−8.11 −14.14 −14.04 −14.28 −13.85 −11.46 −13.86 −7.47 −15.37 −15.30 −17.76 −15.41 −17.52 −20.49 −21.88 −21.25 −18.38 −19.99 −17.72 −17.85 −18.06 −18.26 −18.40 −15.40

2.30 62.14 62.68 58.68 62.34 62.04 60.59 21.43 38.26 77.03 76.15 96.84 115.82 114.35 115.70 114.11 99.63 99.39 100.49 99.86 98.69 98.90 99.04 99.75

−6.72 −12.57 −12.47 −13.77 −12.38 −12.53 −13.40 −10.08 −11.32 −14.43 −14.83 −17.08 −17.36 −18.12 −17.45 −18.28 −16.28 −16.36 −15.85 −15.82 −16.69 −16.64 −16.54 −16.14

−47970.59 −287487.32 −287487.23 −287487.74 −287487.59 −287487.73 −287487.63 −143744.75 −191714.69 −335458.58 −335457.58 −431231.55 −479202.21 −479200.85 −479199.41 −479200.26 −431230.64 −431230.93 −431231.22 −431230.44 −431229.82 −431231.61 −431229.75 −431229.79

1⇔2 2⇔3 2⇔4 2⇔5 2⇔6 + 6 2⇔8 6⇔7 6 + 7⇔8 6 + 7⇔9

−611.13594 −611.13746 −611.13444 −611.13525 −611.13437 −687.61010 −458.47242 −687.59672 −687.60070

−21.47 −20.76 −20.59 −19.65 −20.24 −20.65 −20.74 −25.77 −24.60

15.74 87.28 87.61 86.21 87.10 87.09 87.39 41.58 60.90 105.88 105.81 130.99 150.54 150.58 150.59 150.67 132.19 132.10 132.18 131.50 132.07 132.17 132.11 132.03 Transition states 115.86 116.16 116.25 116.21 114.52 135.57 90.07 134.64 133.84

84.98 85.61 84.54 84.93 82.09 101.25 62.15 99.37 98.94

−15.44 −15.28 −15.86 −15.64 −16.22 −17.16 −13.96 −17.64 −17.45

−383414.72 −383414.50 −383412.92 −383412.32 −383414.62 −431384.18 −287640.47 −431382.31 −431384.25

H2O 1 eq/eq ax/ax

followed by a discussion comparing the experimental and computational results. In general, we find relatively good agreement in the thermodynamically calculated free energies in solution with the NMR equilibrium distribution. The free energies of some of the ground state dimeric structures are very close, certainly within the computational error, and therefore cannot be distinguished as reliably. The calculated barriers, although slightly overestimated, are in relatively good agreement compared to known experimental barriers. Overall, our results suggest that the computational protocol is feasible and has reasonably good predictive power; however, the approximations and potential errors in this approach must be taken into consideration.

account for the free energies in solution. Details are provided in the Computational Methods section. Although glycolaldehyde trimers are expected to have very low concentrations in a 1 M glycolaldehyde solution, we calculated the free energies of the trimers that could potentially be formed in solution. Acyclic trimers can be formed by the addition of glycolaldehyde monomer (6 or 7) to an acyclic dimer (2, 8, 9) as shown in Figure 2. Cyclic trimers can be formed in two ways. Glycolaldehyde could add to the cyclic dimers producing six possible cyclic trimers (see 15−20 in Figure 3). On the other hand, the acyclic trimer 10 could close to form the five-membered rings 21 and 22 (Figure 3). The NMR experiments were time-course reactions of hydrolyzing glycolaldehyde acetal dimer to form a 1 M solution of glycolaldehyde monomer equivalents. Peak areas were then integrated to determine concentrations of each species in solution, guided by a previous NMR study of monomers and dimers performed by Glushonok et al. (1986).43 We also determined the concentration of the most stable trimers predicted by the computations. Details are provided in the Experimental Methods section. This paper is organized as follows. After detailing the computational and experimental methods used, we present the analysis of our NMR data. The calculated thermodynamic and kinetic energy landscape using our protocol will then be shown,

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METHODS AND MATERIALS Experimental Methods. Solutions containing 1.0 M of glycolaldehyde monomer were prepared by mixing the crystalline glycolaldehyde dimer 1 (Aldrich) with D2O (Cambridge Isotope, 99.9% D) immediately before NMR analysis (t = 0). Acetonitrile (Aldrich, 1% v/v) was used as an internal standard for determining chemical shifts and for calculating concentrations. NMR spectra were collected at 298 K on a Varian 500 MHz instrument with a relaxation delay of 1 s. Relaxation delay times between 1 and 10 s were tested, with no signal attenuation. Spectra were processed using an 3000



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Figure 4. 1H NMR spectrum of 1 M glycolaldehyde at equilibrium, 9 h after mixing dimer 1 in D2O. Monomer peaks are labeled in green, acyclic dimers in blue, and cyclic dimers in red. Trimers are represented by the letter “T” in black. The complete 1H NMR spectra is also provided in Figure S4, Supporting Information.

exponential window function with no line broadening. The first data were recorded within 7 min of mixing and averaged over 3 min. Averaging times were increased during the run: after 3 h, samples were near equilibrium and 50-min averages were recorded. The final measurement was taken 10.5 h after mixing. No significant differences in line shape were observed for the duration of the experiment. The MestreNova Lorentzian− Gaussian peak-fitting algorithm was utilized to determine peak areas of the smaller and overlapping peaks. Peak assignments of monomers and dimers were performed following the work of Glushonok et al. (1986).43 Signal to noise ranges from 49.5 (trimer peak at 5.36 ppm) to 4979.0 (7). Computational Methods. All calculations were carried out using Jaguar 6.044 at the B3LYP45−48 flavor of density functional theory (DFT) with a 6-311G** basis set. A comparison of our protocol to other levels of theory in a similar system involving aldehyde oligomerization is provided in ref 40. To maximize the probability of finding the global minimum, we performed calculations on various conformers of each structure with different internal hydrogen bond networks. Higher energy conformers are only included where relevant in the discussion. The electronic energy of the optimized gasphase structures is designated Eelec in Table 1. The Poisson−Boltzmann (PB) continuum approximation49,50 was used to describe the effect of solvent. Similar to our previous studies, we chose water with the following parameters: a dielectric constant of 80.4 and a probe radius of 1.40 Å. The forces on the quantum mechanical solute atoms due to the solvent can be calculated in the presence of the solvent. However, in this work, the solvation energy was calculated at the optimized gas-phase geometry because in many cases there is practically no change between the gas phase and implicit solvent optimized geometries. This comparison was made in our previous studies in similar oligomerization reactions involving small aldehydes.18,39,40 The solvation energy is designated Esolv in Table 1. It is important to note that even though the solvation energy contribution is to some extent a free-energy correction, it certainly does not account for all of the free energy. The analytical Hessian was calculated for each optimized structure, and the gas-phase energy corrected for zero-point vibrations. Negative eigenvalues in transition state calculations were not included in the zero-point energy (ZPE). The temperature-dependent enthalpy correction term is straightforward to calculate from statistical mechanics where we assume

that the translational and rotational corrections are a constant times kT, that low frequency vibrational modes will generally cancel out when calculating enthalpy differences, and that the vibrational frequencies do not change appreciably in solution. The combined ZPE and enthalpy corrections to 298 K are designated Hcorr and the corresponding gas-phase free energy correction to 298 K is designated Gcorr in Table 1. The corresponding free-energy corrections in solution are much less reliable.51−53 Changes in free energy terms for translation and rotation are poorly defined in solution, particularly as the size of the molecule increases. Additional corrections to the free energy for concentration differentials among species (to obtain the chemical potential) can be significant, especially if the solubility varies among the different species in solution. Furthermore, since the reactions being studied are in solution, the free energy being accounted for comes from two different sources: thermal corrections and implicit solvent. Neither of these parameters is easily separable, nor do they constitute all the required parts of the free energy under our approximations of the system. To estimate the free energy, we followed the method of Lau and Deubel54 who included the solvation entropy of each species as half of its gas-phase entropy. Wertz42 and Abraham41 had previously suggested that upon dissolving in water, molecules lose a constant fraction (∼0.5) of their entropy. In Table 1, this is designated −0.5TScorr and is calculated by 0.5(Gcorr − Hcorr). Recent computational studies in other unrelated systems have come to the same conclusion.55,56 The free energy of each species, designated G298, is the sum of Eelec, Esolv, Hcorr and −0.5TS. Our reported ΔG values are calculated from the difference in G298 between the reactants and products, and therefore include the zero-point energy, enthalpic and entropic corrections to 298 K for a reaction in solution. In our previous studies, we found that this protocol for calculating ΔG provided good agreement with experiment for the hydration of formaldehyde (although the calculated barriers were systematically too high), and for the equilibrium constant comparing between the monohydrate and dihydrate forms of methylglyoxal.40 As mentioned in the introduction, the purpose of this study is to subject this to a more detailed comparison between theory and experiment. Raw data for the electronic energy of the optimized gasphase structures, Poisson−Boltzmann solvation energy, ZPE and thermodynamic corrections to 298 K, for the structures with the lowest free energies are available in Table 1. Besides 3001



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the ground state values for the two monomers and seven dimers shown in Figure 1, the open (linear) trimers (Figure 2), and all relevant transition states are included. Note that for 1, having both hydroxyl groups in the equatorial positions is just marginally more stable than having them both in the axial position. In analyzing the results, we will essentially use the conformer with the lower G298 value. The difference of 0.09 kcal/mol is certainly within the computational error. In fact, all the lowest energy ring structures have energies within a 0.40 kcal/mol spread and, given the approximations in our protocol, can be considered to be of similar energy. For transition state calculations, two additional catalytic water molecules were explicitly added to the system to find the lowest energy barrier for proton transfers − this corresponds to an eight-center transition state as discussed below. All calculated transition states have one large negative eigenvalue corresponding to the reaction coordinate involving bond breaking/forming and accompanying proton transfer. Each optimized transition state was checked to make sure that this negative frequency eigenvector indeed corresponded to the correct reaction linking reactant to product. Reaction energies and equilibrium constants, including concentration corrections required for a 1 M solution, are discussed in the Results section.

Figure 6. Time-dependent concentrations of acyclic glycolaldehyde dimers.

dimer 2 (the key intermediate allowing for interconversion among the ring oligomer structures) is at a constant concentration of 0.002 M over the entire experiment. The aldehyde group in this dimer also undergoes hydration to form the hydrated dimer 8 containing a terminal gem-diol. Glushonok et al. (2000) found that both 2 and 8 increased sharply to approximately 0.01 M within the first 3 min, and then while the concentration of 2 declines, the concentration of 8 continues to increase but much more gradually until reaching an equilibrium value of 0.027 M.57 In this work, the concentration of 8 does increase sharply for the first 16 min, but then decreases to an equilibrium value of 0.028 M while the concentration of 2 maintains an equilibrium value of 0.002 M (Figure 6). Difficulties in quantifying the acyclic dimer 2 peak due to the overlap with a larger peak from the glycolaldehyde monomer 6 may be the cause of this discrepancy. The acyclic dimer 2 favorably hydrolyzes into two monomers of glycolaldehyde 6. We see an increase in concentration of 6 that starts to level off after ∼2 h (Figure 7). Given that there is

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RESULTS AND DISCUSSION NMR Measurements of Species Concentrations. The 1 H NMR spectrum of 1 M glycolaldehyde in D2O is shown in Figure 4. Peak assignments refer to structures shown in Figure 1. As the monomer and dimer assignments in this work followed those of Glushonok et al.,43,57 and the numbering schemes between these works differ, equivalent figures that include each numbering scheme are provided in Supporting Information. In the NMR monitoring of the hydrolysis of the sixmembered ring dimer 1, we see a progressive drop in its concentration, as expected (Figure 5). All other species should

Figure 5. Time-dependent concentrations of cyclic glycolaldehyde dimers.

Figure 7. Time-dependent concentrations of glycolaldehyde monomers and starting dimer.

start at zero M at t = 0. In spite of the 7 min time lag between mixing and data collection, we were able to measure the initial rise in concentrations of most species, with the exceptions of dimers 2, 4, and 5 (Figures 5, 6). The initial appearances of these dimers were, however, observed by Glushonok et al. (2000).57 After several more minutes of reaction, we observe a progressive decrease in the concentrations of all four ring species to equilibrium concentrations of 0.02−0.03 M (1, 3 and 4) and 0.061 M (5) after 3 h. The concentration of the acyclic

plenty of water in a 1 M solution, it is not surprising to see a concomitant increase in the hydrated monomer 7. The equilibrium concentrations of 6 and 7 after 3 h are 0.037 and 0.55 M, respectively. Therefore, the measured equilibrium constant for glycolaldehyde hydration is 14.9 ± 0.4, in reasonable agreement with 18 ± 3.3, calculated by Glushonok et al. (1986)43 and reasonably close to 17.5, observed by Collins and George for a 0.1 M solution.58 3002



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hydration come to the conclusion that the 8-center transition state is indeed the most favorable.59 The actual structure of the eight-center glycolaldehyde hydration transition state is shown on the right side of Figure 8 with bond distances in Å. The newly forming C−O bond distance is 1.65 Å, the CO has lengthened to 1.30 Å, and the O−H bonds being made and broken are between 1.11 and 1.34 Å. The lowest energy conformation, as shown in Figure 8 and having the corresponding energies listed as 6⇔7 in Table 1, has the vicinal hydroxyl cis to the carbonyl oxygen forming a weak intramolecular hydrogen bond. Two water molecules assist in the proton transfer. The energy barrier, given by the difference between G298 of the transition state and glycolaldehyde +3 H2O, is −287640.47 + (143744.75 + 3(47970.59)) = 16.05 kcal/mol. The corresponding barriers for having zero, one, and three water molecules (i.e., 4-center, 6-center and 10-center transition states) are 40.83, 24.37, and 19.89 kcal/mol respectively. Energies and structures for these higher-energy transition states may be found in Supporting Information. The reaction free energy of hydration is given by the difference between G 298 of the hydrate compared to glycolaldehyde + H2O, that is, −191714.69 + (143744.75 + 47970.59) = 0.66 kcal/mol. This reaction would indeed be slightly endergonic if the concentration of glycolaldehyde and water were equal. However, in a 1 M solution, water is 55 times more “concentrated” than glycolaldehyde so the hydration reaction is actually exergonic when we apply an appropriate concentration correction. The correction factor and the caveats in such an approximation are discussed in detail below. Using the G298 values from Table 1, we can calculate the change in free energy ΔGrxn and the activation barrier ΔG⧧rxn for the individual reactions in Figure 1. Because the trimers are very minor species in an aqueous glycolaldehyde solution, we have only calculated the barriers relevant to the monomers and dimers. These are shown in Table 2. While this is useful when focusing on particular reaction steps, they do not provide an overarching view of the overall energy landscape.

Glycolaldehyde 6 and hydrate 7 can also form the dimers 8 and 9 if a hydroxyl on 7 attacks the carbonyl of 6. If the gemdiol of 7 is the attacking group, the resulting dimer 9 is one that does not itself contain a gem-diol, and therefore does not easily dehydrate (or cyclize). The gem-diol containing dimer 8 can therefore be formed either from hydration from the acyclic dimer 2 discussed earlier, or by dimerization of monomers. The hydrated dimers 8 and 9 reach equilibrium concentrations of 0.028 and 0.011 M within 3 h. The equilibrium constant between the two dimers is 2.5 ± 0.5. Trimers, both cyclic and acyclic can be formed as shown in Figures 2 and 3. The NMR data shows many small peaks that were not identified as dimers or monomers by Glushonok et al. (1986);43 these are likely trimeric species. The singlet at 4.29 ppm, doublet at 3.36 ppm and triplets at 4.87, 5.20, and 5.37 ppm are assigned to the proposed trimers shown in Figures 2 and 3 (see Figure 4). It is unclear which trimer corresponds to which peak, but the time series and concentration data are consistent with expectations for the formation of trimer species. These peaks are labeled “T” in Figure 4. Low concentrations of trimers, relative to dimers, are expected, analogous to the dominance of monomers over dimers in 1 M solution, all due to oligomer hydrolysis. Since the concentrations of the ring structures (1, 3, 4, 5) drop rapidly while the concentrations of the monomers and acyclic dimers (2, 6, 7, 8, 9) increase at a rate of ∼7 mM/min (mostly due to 7), the concentrations of trimers (especially 11 and 12) should initially increase with time. Indeed, the peaks assigned to the trimers do increase slowly, with the peaks at 3.36 and 5.20 ppm each reaching final concentrations of 0.007 M. According to our computations (discussed below), we predicted that two of the trimers would have small but significant concentrations (>0.005 M), and indeed this is what we observe experimentally. In addition, the calculated sum of the concentrations of the five most abundant trimers (0.017 M) is close to the total observed concentration of these five NMR peaks (0.020 M). Free Energy Changes from Computational Chemistry. There is basically one type of reactionnucleophilic attack of the carbonyl carbon by a water molecule or hydroxyl group and its accompanying reverse reaction. The attacking nucleophile oxygen atom transfers its attached proton to the oxygen of the carbonyl. The most stable transition states have two intervening water molecules facilitating the proton transfer leading to an eight-center transition state as shown in Figure 8 on the left. In the case of a hydration reaction R′ = H, and in a ring-closing reaction, R and R′ are part of the same molecule. Extensive computational work by Wolfe et al. at the MP2//6-31G* level studying the different transition states of formaldehyde

Table 2. Reaction Free Energy Changes and Barriers reaction 1 2 2 2 2 2 6 6 6

→2 →3 →4 →5 →6+6 + H2O → 8 + H2O → 7 +7→8 +7→9

ΔGrxn (kcal/mol)

transition state

ΔG⧧rxn (kcal/mol)

−0.42 +0.16 +0.12 +0.02 −1.76 −0.24 +0.66 +0.86 +1.86

1⇔2 2⇔3 2⇔4 2⇔5 2⇔6 + 6 2⇔8 6⇔7 6 + 7⇔8 6 + 7⇔9

13.79 14.43 16.01 16.61 14.31 15.34 16.05 16.37 18.31

From the computational results, the hydrolysis of the initial ring dimer 1 to the acyclic dimer 2 is thermodynamically favorable and has a relatively low barrier of ∼14 kcal/mol. The acyclic dimer 2 can undergo ring closure to form the sixmembered ring 3 with one axial and one equatorial hydroxyl group. If the terminal hydroxyl in 2 does not act as the nucleophile, but rather the other hydroxyl group, then the fivemembered rings 4 and 5 can be formed. In the “cis” structure 5, there is an intramolecular hydrogen bond between the OH and CH2OH groups on the same side of the ring. The difference in energies of these other ring structures relative to 2 is tiny, and certainly within the computational error. The lowest energy

Figure 8. Generic 8-center and glycolaldehyde hydration transition state. 3003



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carefully distinguish these relative free energies from the isolated reaction energies described in Table 2, we have dropped the “rxn” subscript and also report our values to just 1 decimal place (since the computational error is larger than 0.1 kcal/mol given the approximations). The relative free energies for the monomers and dimers are shown in Figure 11 with ΔG

transition states for all four ring-closing/opening reactions are shown in Figure 9. The barriers to the five-membered rings are slightly higher (∼16 kcal/mol) than to the six membered rings (∼14 kcal/mol).

Figure 9. Ring-opening/closing transition states.

The acyclic dimer 2 can also hydrolyze into its monomers. This is a favorable reaction in which ΔGrxn is −1.76 kcal/mol, and the barrier is ∼14 kcal/mol. Hydration of 2 leading to the dimer hydrate 8 is also favorable, ΔGrxn is −0.24 kcal/mol, and the barrier is ∼15 kcal/mol. Another way that 8 can be formed is by the reaction of the monomer 6 and its hydrate 7 wherein the hydroxyl that is not part of a gem-diol acts as the nucleophile. If however one of the gem-diol hydroxyl groups acts as the nucleophile, then the dimer hydrate 9 is formed. This hydrate is both less stable thermodynamically and kinetically less accessible, and is not expected to easily undergo dehydration as it does not have a gem-diol in its structure. The transition states for 2⇔6 + 6 and 6 + 7⇔8 are shown in Figure 10.

Figure 11. Relative free energies (kcal/mol) of the monomers, dimers and transition states.

values written below each species, and transition state relative free energies, ΔG⧧ in italicized font and written next to a double-headed arrow connecting the two species. Although unhydrated monomeric glycolaldehyde 6 is the thermodynamic sink in this scheme, because this is a 1.0 M solution, there is plenty of water in the system and therefore the monomer hydrate 7 is the predominant species in solution at equilibrium. Glushonok et al. (2000) measured the forward and reverse rate constants for hydration of 6 to 7 and reported values of 1.55 × 10 −4 M −1 s −1 and 4.90 × 10 −4 s −1 respectively.57 At equilibrium, kfwd[6][H2O] = krev[7]. If the relative amounts of glycolaldehyde and water were approximately equal, then the equilibrium constant would be 1.55/ 4.90 = 0.316 which corresponds to ΔGrxn = +0.68 kcal/mol at 298 K (using ΔGrxn = −RT ln Keq), very close to the computed +0.66 kcal/mol. However since water is 55 times more abundant in a 1.0 M solution, the experimental equilibrium constant is 0.316 × 55 = 17.4. The concentration correction is −RT ln(55) or −2.37 kcal/mol when the gem-diol hydrate (having an additional H2O in its structure) is compared to its aldehyde. Taking this into account, one could find that the difference in computed free energy between glycolaldehyde and its hydrate should be +0.66 − 2.37 = −1.71 kcal/mol, which leads to a computed equilibrium constant of 17.9 in favor of the hydrate. This compares very well to the equilibrium constant reported by Glushonok et al. (1986) and to our experimental measurements with values of 18.0 and 14.8, respectively.43 The comparison of the barrier to the rate constant is not as straightforward because it requires knowing the pre-exponential factor in the Arrhenius equation. Winkelman et al.60 measured the rate constant for dehydration of methylene glycol reporting that krev = 4.96 × 107 exp(−6705/T) in the 293−333 K and pH 6.0−7.8 range. If we assume that the hydrate of glycolaldehyde

Figure 10. Transition states for oligomerization.

Energy Landscape from Computational Chemistry and Comparison to Experiment. A useful rendition of the data from Table 2 is to choose a set of reference molecules and compare the energies of all species to this reference set. Since glycolaldehyde monomer has the lowest energy in this scheme, and water is always present in the system, we assign glycolaldehyde and water as the reference states assigning them a relative solution free energy, ΔG = 0.0 kcal/mol. To 3004



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Table 3. Relative Energies, Correction Factors and Concentrations in a 1 M Solutiona

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

ΔG (kcal/mol) from Figure 9

hydrate correction (kcal/mol)

2.18 1.76 1.92 1.88 1.78 0 0.66 1.52 2.52 2.71 2.64 4.00 5.44 4.58 3.62 3.33 3.03 3.82 4.44 2.64 4.47 4.09

−1.96 −1.96 −1.96 −1.96 −2.37 −1.96 −1.96 −1.72 −1.72 −1.72 −1.72 −1.72 −1.72 −1.72 −1.72 −1.72 −1.72 −1.72 −1.72

conc. corrected values

rescaled values

relative concen-tration (normalized to 1 M)

estimated Glushonok57 experiment-al values (M)

0.22 1.76 −0.04 −0.08 −0.18 0 −1.71 −0.44 0.56 2.71 0.92 2.28 3.72 2.86 1.90 1.61 1.31 2.10 2.72 0.92 2.79 2.37

1.93 3.47 1.67 1.63 1.53 1.71 0.00 1.27 2.27 4.42 2.63 3.99 5.43 4.57 3.61 3.32 3.02 3.81 4.43 2.63 4.46 4.08

0.0198 0.0015 0.0307 0.0329 0.0389 0.0287 0.5159 0.0604 0.0112 0.0003 0.0061 0.0006 0.0001 0.0002 0.0012 0.0019 0.0031 0.0008 0.0003 0.0061 0.0003 0.0005

0.02 0.002 0.03 0.03 0.06 0.034 0.62 0.027 0.01

experimental values (1 M solution) (M) 0.0276 0.0020 0.0205 0.0278 0.0611 0.0369 0.545 0.028 0.0119 0.0199 0.0199 0.0199 0.0199 0.0199 0.0199 0.0199 0.0199 0.0199 0.0199 0.0199 0.0199 0.0199

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.0016 0.0004 0.0024 0.0008 0.0014 0.0009 0.009 0.003 0.0023 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011

a

Experimentally determined trimer peaks have been added together and presented as one data point due to the uncertainty in peak assignments. They have been accounted for in the normalization to 1 M.

magnitude suggesting that our calculations may be overall in the right regime. In addition, Glushonok et al. (2000) do not detail how they calculated the rate constants from the species concentration changes as a function of time studied by NMR.57 A clearer comparison may be possible by calculating the expected equilibrium concentrations of all species in solution based on their computed free energies, and then comparing these to the experimental concentrations. Relative Concentrations from Computational Chemistry and Comparison to Experiment. As described above, because water is both a reactant and a solvent, we need to make the appropriate free energy corrections to correctly calculate the equilibrium constants, and hence the equilibrium concentrations of each species. Now if we apply the −2.37 kcal/mol concentration correction factor to glycolaldehyde hydrate 7, then its concentrated-corrected ΔG values would be −1.7 kcal/mol. For the hydrated dimers we added a −1.96 kcal/mol corresponding to −RT ln (55/2) since our reference state is to a 1 M solution of the monomer, that is, one could consider the hydrated dimer to have a monomer to water ratio of 2:55. Because the cyclic dimers do not dehydrate, we also assigned them the same correction factor. We do not have strong justification for this latter correction, although it seems to be an approximation that provides good results in comparison with experiment. Further discussion, including the use of different correction factors, can be found in Supporting Information. Similarly for the hydrated trimers, we added −1.72 kcal/mol corresponding to −RT ln (55/3). We have compiled these correction factors in Table 3 below (with additional decimal places so that the calculations are clear these decimal places do not speak to the precision of the computed numbers). Since the relative energies of the trimers, with the exception of 11, 17, and 20 are over 3 kcal/mol higher than the most stable structure 7, their relative equilibrium

monomer has a dehydration reaction with roughly the same pre-exponential factor of ∼5 × 107, then our computed rate constant of krev is 2.50 × 10−4 s−1. This is half the value found by Glushonok et al. of 4.90 × 10−4 s−1, although certainly within the same order of magnitude. For comparison, the computed and experimental dehydration barriers would therefore be 15.39 and 15.01 kcal/mol respectively. For hydration of the acyclic dimer (2 + H2O → 8), the measured rate constants by Glushonok et al. (2000) for the forward and reverse rate constants are 2.02 × 10−4 M−1s−1 and 1.47 × 10−4 s−1 respectively.57 Using the same analysis as we did for the monomer, the ratio would be 0.202/0.147 = 1.37 which corresponds to ΔGrxn = −0.19 kcal/mol at 298 K, again very close to the computed −0.24 kcal/mol. Assuming that the dehydration reaction has a pre-exponential factor of ∼5 × 107 leads to a computed rate constant of krev of 1.87 × 10−4 s−1, just slightly larger than the experimental value. These results suggest that, at least for the hydration/ dehydration reactions of glycolaldehyde (monomer and dimer), our protocol works quite well and is in good agreement with experimental data for both the relative free energies and the barriers. Our calculations also match experimental results well for the equilibrium constant if we add the −RT ln(55) or −2.37 kcal/mol correction for a 1 M solution. On the other hand, there seem to be larger discrepancies for the dimerization reactions and ring-opening/closing reactions with differences in ΔGrxn of the order of 1−2 kcal/mol, which is a significantly more severe 5 to 30-fold difference in equilibrium constants. We did not compare the rate constants for these other reactions because it is unclear what the pre-exponential factor should becertainly not 5 × 107, and probably of the order of 109− 1011. In terms of the overall landscape however, the computed barriers are in roughly the same regime, mainly in the 14−16 kcal/mol range and the rate constants span just 2 orders of 3005


The Journal of Physical Chemistry A concentrations (along with larger oligomers) are expected to be less than 0.002 M, and their relative contributions negligible. Since the monomer hydrate 6 has the lowest concentrationcorrected solution free energy, we have rescaled the values so that it has a relative energy of zero. We can then calculate the relative concentrations of all 22 species using the Boltzmann equation Ci/C0 = exp (-ΔGi/RT), normalizing the results to ensure that in a 1.0 M solution, Cm + 2Cd + 3Ct= 1 where m, d, and t stand for monomer, dimer, and trimer forms of glycolaldehyde, respectively. The third-from-right column represents these computed concentrations at equilibrium. Given the approximations inherent in the protocol, the magnitude differences in relative concentrations of the four ring-dimer species (1, 3, 4 and 5) ranging from 0.02 to 0.04 M are probably not significant and could be considered computationally indistinguishable. The second-from-right column comes from data by Glushonok et al. (2000) at t = 2.5 h; however, from their graphs, it is not clear that the system had reached equilibrium by this point.57 The rightmost column in Table 3 summarizes our measured equilibrium concentrations, which are within 50% of those of Glushonok et al.57 This suggests that their numbers are not far from equilibrium values. From Figures 5−7, we see that all species reach equilibrium between 2.5 and 3.5 h after mixing. A comparison between the computed and experimental concentrations suggests reasonably good agreement. In particular, the monomer concentrations of 0.52 and 0.029 M are close to the experimental values of 0.55 and 0.037 M. There is also relatively good agreement in the dimer concentrations, with the exception of 8 where the computational value is slightly larger than twice the experimental values taken from both studies. Both NMR studies find that 5 is the most stable of the ring dimers, in agreement with computations. The concentration ranges are also quite similar for these dimers, 0.02−0.04 M computationally and 0.02−0.06 M from both sets of NMR experiments. There is, perhaps surprisingly, good agreement between computation and experiment for the two least stable dimer structures, 2 and 9, that have low concentrations of 0.002 and 0.01 M respectively. In addition the computed concentrations for the acyclic trimer 11 and cyclic trimer 20 of 0.0061 M agree reasonably well with the experimental concentration from the NMR peaks at 3.36 and 5.20 ppm of 0.007 M. There are other peaks visible on the NMR spectrum (see Figure 4), likely caused by other trimers present at even lower concentrations. Overall, our computational protocol does relatively well at predicting the equilibrium concentrations of all species in solution. The differences between the computational and experimental values are mostly less than 50%, with the exception of 8 (where the difference is approximately 2-fold). This system, however, is relatively simple with only 8 species with concentrations over 0.01 M, and it is unclear if our protocol will show as good an agreement for larger and more complex systems. A system with multiple reactants, each with different concentrations and activity coefficients, will present an additional challenge to this protocol. Figure 11 may serve as a first-approximation thermodynamic and kinetic map even though the relative free energies are not concentrationcorrected. We are currently studying more complex oligomerization reactions to examine if our computational approach is able to provide insight into the complex product distributions observed experimentally.

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CONCLUSION

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ASSOCIATED CONTENT

Article

In this study, we compared the efficacy of a computational protocol to map the thermodynamic and kinetic landscape of glycolaldehyde in solution. Glycolaldehyde is an ideal test case because it is primarily dominated by monomers and dimers in solution. Comparing our computed solution free energies to equilibrium concentrations determined by NMR measurements, we find overall good agreement, suggesting that at least for glycolaldehyde oligomerization, our calculated energies represent the system well. Computational chemistry is useful in studying complex systems with large product distributions because we can tease out and identify the energetic contributions of the many different species in a reaction mixture. In this study, our approach predicted that one of the trimers would have a small but appreciable equilibrium concentration, and this was consistent with NMR measurements. The study of oligomerization reactions involving multiple species is one in which collaborative efforts between computational and experimental work could lead to an improved understanding of these complex systems. Although our results suggest that this protocol is feasible and has reasonably good predictive power, there are numerous approximations and therefore some potential errors that must be carefully weighed in the final analysis.

* Supporting Information S

XYZ coordinates of the most stable structures, tables showing the effect of different correction factors, additional NMR spectra, and a comparison of different labeling schemes previously used in the literature. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ‡

Yale-NUS College, 6 College Avenue East #B1-01, Singapore 138614. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by a Camille and Henry Dreyfus Teacher-Scholar award (J.K.) and NSF grant AGS-1129002 (M.M.G, D.O.D.H.).

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Glycolaldehyde Monomer and Oligomer Equilibria in Aqueous

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